Resource Library

This model illustrates a projection of property damages and human costs from potential natural disasters over a 5-year period that might be assessed by an insurance company. It assumes that each disaster either occurs or doesn't occur in a given year with given probabilities. Then possible property damages and possible human costs are simulated. In each of these, assuming that a disaster occurs, the total damage or cost is composed of the random number of people affected and the damage or cost per person affected._x000D_

This model assumes that an insurance company is offering a local organization an insurance policy that will guard the organization against large heating oil costs from excessively cold winters. There are three sources of uncertainty: the price of heating oil, the weather, and the amount of heating oil required. The first two of these are modeled with @RISK's Time Series Fit tool, based on real historical data.

This model uses @RISK to run a discrete-event simulation of insurance claims through time. It assumes that a company starts with an initial number of customers and an initial amount of cash. There are three types of events, and the times between each are assumed to be exponentially distributed. A type 1 event is when a customer makes a claim for a random amount, a type 2 event is when a current customer leaves the company, and a type 3 event is when a new customer joins the company. All of the company's customers pay a premium at a given daily rate.

This model enables an insurance company to analyze the possibility of being reinsured. Without reinsurance, the company pays all claims, net of deductibles, for its policy holders. With reinsurance, it pays a fixed premium to another insurance company, the reinsurer. There is a reinsurance deductible. If the company's liability for all claims, net of deductibles, is less than this deductible, the company is liable for all of it. However, if this liability is greater than the reinsurance deductible, the company is liable only for the deductible; the reinsurer pays the rest._x000D_

This model contains a portfolio of potential claims of different types. Each claim has different parameters for the distributions of frequency, severity, and duration. The model illustrates a powerful feature of the RISKCOMPOUND function: the argument that corresponds to the severity can be a reference to a cell containing a formula, rather than just a single distribution function.

This example shows how you might model the uncertainty involved in payment of insurance claims. To model this properly, you must account for the uncertainty in both the total number of claims and the dollar amounts of each claim made. This is done using the RiskCompound function.
Suppose that the company is required by law to have enough money on hand to pay all the claims with the probability of 95%, and that it can only set aside $2000 for the purposes of this particular insurance product. On the other hand, a simulation of the model shows that the 95th percentile of the Total Payment Amount is around $2700. Assume further that the company can purchase from a larger company an insurance policy against the number of claims being in the top decile. The policy under consideration specifies that if the number of claims falls within the top decile, the larger company will satisfy all the claims. The smaller company can model the situation with the policy in place by using Stress Analysis to stress the distribution for total number of claims from the 0th to 90th percentile. With the modified distribution the 95th percentile of the Total Payment Amount is reduced to around $1650. If the policy costs up to $350, the smaller company can purchase it and keep $1650 on hand to comply with the law.
Would the larger company be willing to sell the policy for under $350? There is a 10% probability that it will be required to make payments under the policy. The payments can be analyzed using the same model and stressing the distribution for total number of claims from the 90th to 100th percentile. This analysis shows the mean payment to be around $2800. Since there is only a 10% probability that claims will need to be satisfied, the mean cost to the larger company is around $280. Hence, it does not seem unreasonable for the larger company to sell the policy for $350.

This example models different types of insurance claims from different lines of business and sums them in order to calculate an estimated total claims paid out for the next year. It incorporates @RISK distribution fitting to define distribution functions for claim amounts, and illustrates the use of correlations to describe relationships between different types of claims. The RiskCompound function is used to combine frequency and severity of claims, simplifying the model.

A model for evaluating a contingent contract, where a penalty must be paid if a target is not met.

It is important for an insurance company to estimate the amount of claims it will incur in a given year. Here you will find a set of examples to model this problem:
1. A deterministic model to get started.
2. A na•ve @RISK model that fails to capture all the uncertainty in total claims.
3. A better version using the RiskCompound function to capture all of the uncertainty in total claims.
4. A version using the method of resampling to simulate the numbers of claims each year.
Click here to see a video of this example.

An insurance model that illustrates @RISK's Stress Analysis feature.
Click here to see a video of this example.

TopRank recognizes @RISK distribution functions and incorporates them in What-If analyses. This ability provides more flexibility and accuracy in modeling the possible input values in your What-If analysis. In this example, Jupiter Corporation is building a new model of 4-door sedan. Assuming that the car will generate sales for the next 5 years, management has identified 5 factors that can influence the total revenue during that period. Several of these factors have probability distributions associated with them. During a What-If analysis, TopRank sees the probability distributions associated with these items and performs a smart sensitivity analysis using them, stepping through the range of the distribution while spacing the steps such that each interval encompasses equal amounts of probability.

This model represents the process flow of a company's internal sales quotation process. The process is taken from an actual company and has over 36 individual steps involving 10 individuals or departments. For example, when management saw from the simulation results that it took over 24 hours to complete 35 minutes of value-added work, they saw the need for process improvement.